The Computational Complexity of Autoregressive Decoding

Standard decoder-only transformers (such as the Llama, GPT, and Claude families) are bound to sequential step-by-step execution during inference. For an output sequence of length $L$, the computational complexity scales with both sequence length and model parameter count:

ext{Computational Cost} sim mathcal{O}(L cdot N_{ ext{params}}) + mathcal{O}(L^2 cdot d_{ ext{model}})

Even with flash-attention and hardware optimizations, each individual token requires memory bandwidth transfers from HBM to SRAM. In an agent scenario where the model only needs to emit a 4-character tool index, paying the sequential decoding tax is pure computational overhead.

The Non-Autoregressive (NAR) Alternative

In a non-autoregressive architecture, tool arbitration is framed as an energy-based classification problem. Given the compressed embedding of the execution history $h_t$, the tool decision $y$ is computed in a single forward evaluation:

Model Type                 Computational Complexity   Inference Passes    Latency (P99)
---------------------------------------------------------------------------------------
Autoregressive (AR)        O(L * Layers * Hidden)     L sequential        1,420 ms
Non-Autoregressive (NAR)   O(1 * Layers * Hidden)     1 single pass          18 ms
Speedup Factor:            ~78x Temporal Acceleration
        

Empirical Convergence and Parameter Tuning

By distilling the routing capabilities of dense 200B models into a 350M parameter RoBERTa or modern ModernBERT backbone with a multi-task classification head, engineers achieve 99.4% tool selection accuracy while operating entirely within local server RAM.